Without limiting the scope of the invention, its background is described in connection with a scheme for demodulating a composite frequency modulation (FM) stereo signal, as an example.
A composite FM stereo signal is of the form: EQU fm(t)=[l(t)+r(t)]++Apsin(.omega..sub.p t)+[l(t)-r(t)]sin(2.omega..sub.p t)EQ'N 1
where:
fm(t) is the time varying value of the composite signal; PA0 l(t) is the time varying value of the left channel signal; PA0 r(t) is the time varying value of the right channel signal; PA0 A.sub.p is the amplitude of the 19 KHz pilot signal; PA0 .omega..sub.p is the pilot frequency of 2.pi.*19 K radians per second (19 KHz).
FIG. 1 illustrates a frequency spectrum of a typical FM stereo composite signal showing the components of Equation 1. The components include a sum of the left and right channel signals covering a 15 KHz bandwidth from DC to 15 KHz and the difference of the left and right channels modulated to and centered about 38KHz carrier signal, with a 30 KHz bandwidth. Additionally the signal includes a 19 KHz tone signal, commonly referred to as the pilot signal which is used as a reference signal for the radio receiver. The composite signal may also contain subsidiary signals in the 53 KHz to 75 KHz bandwidth such as subsidiary communication authorization (SCA). These signals are excluded from FIG. 1 for clarity.
The composite signal must be separated into left and right channels in order to reproduce the broadcast message in stereo. This requires extracting from the composite signal the values of the left channel and the right channel signals in isolation from the other components of the composite signal. In one method to achieve this the composite signal is decoded by lowpass filtering the signal to extract the [left(t)+right(t)] component; mixing the [left(t)-right(t)] component from 38 KHz (i.e. sin(2.omega..sub.p t)) down to DC; and lowpass filtering the result to extract the [left(t)-right(t)] component. These two components are then input to a matrix which performs arithmetic addition and subtraction to extract the decoded left and right channel signals, one method to separate the composite signal is discussed in Shanmugam, Digital and Analog Communication Systems, .sctn.6.6 (1979). Such an approach is difficult to implement given the sample rate which is required. Since an FM composite signal has at least a 53 KHz bandwidth, a sample rate of greater than 106 KHz (the Nyquist rate)is necessary. This corresponds to only 9.4 us of processing time for filtering. At this sample rate significant amplitude distortion of the signal will result.
Another method to separate the composite signal is disclosed in U.S. Pat. No. 4,723,288 issued to Borth et al. the decoded left and right channel signals can be extracted directly from the composite signal by sampling the composite signal at particular points relative to the pilot signal. Referring again to Equation 1, note that when the 38 KHz carrier signal [sin(2.omega..sub.p t)] equals plus or minus one, fm(t) equals 2 times the left channel signal and two time the right channel signal, respectively, plus the 19 KHz pilot signal term which can be subsequently filtered out. Since the carrier signal is suppressed and since it is synchronized and locked to a harmonic of the pilot signal, the pilot signal can be used to determine when the carrier signal is uniquely plus or minus one. These events occur when the phase of the pilot signal is at an odd multiple of 45.degree.. As can be seen from Equation 1, when the pilot signal phase is at 45.degree. and 235.degree., the value of the composite signal is twice the left signal, and when the pilot signal is at 135.degree. and 315.degree. the value of the composite signal is twice the right signal. In both of these situations the value of composite also contains the component of the pilot signal itself, but this component can easily be filtered out as is well known in the art. When the phase of the pilot signal is detected passing one of these four phase points, the incoming composite signal should be produced.
However, this approach requires that one sample the input signal at very near the exact time that the pilot signal phase is one of the four odd multiple values of 45.degree. as discussed above (corresponding to the carrier signal taking on the value of plus or minus one). If the signal is sampled when the pilot signal phase is off somewhat, the left and right channel recovery is degraded and distortion results. Borth et al. uses a voltage controlled oscillator feedback path to phase lock the sample rate onto the pilot carrier phase and frequency. This approach involves costly and complex hardware for implementation. Additionally, this approach requires the reference frequency of the decoder be a multiple of twice the carrier frequency above 152 KHz.